Model structure learning: A support vector machine approach for LPV linear-regression models

Accurate parametric identification of Linear Parameter-Varying (LPV) systems requires an optimal prior selection of a set of functional dependencies for the parametrization of the model coefficients. Inaccurate selection leads to structural bias while over-parametrization results in a variance increase of the estimates. This corresponds to the classical bias-variance trade-off, but with a significantly larger degree of freedom and sensitivity in the LPV case. Hence, it is attractive to estimate the underlying model structure of LPV systems based on measured data, i.e., to learn the underlying dependencies of the model coefficients together with model orders etc. In this paper a Least-Squares Support Vector Machine (LS-SVM) approach is introduced which is capable of reconstructing the dependency structure for linear regression based LPV models even in case of rational dynamic dependency. The properties of the approach are analyzed in the prediction error setting and its performance is evaluated on representative examples.